TRUCK ARRIVAL MANAGEMENT AT MARITIME CONTAINER …...Dept. of Economics and Business Studies (DIEC)...
Transcript of TRUCK ARRIVAL MANAGEMENT AT MARITIME CONTAINER …...Dept. of Economics and Business Studies (DIEC)...
TRUCK ARRIVAL MANAGEMENT AT MARITIME CONTAINER
TERMINALS
Daniela Ambrosino
Lorenzo Peirano
Dept. of Economics and Business Studies (DIEC)
University of Genova
Via Vivaldi 2, 16126 Genova, Italy
E-mail: [email protected]
KEYWORDS
Truck appointment system, container terminal, mixed
integer linear programming model.
ABSTRACT
In this work the management of truck arrivals in a
maritime terminal is investigated as possible strategy to
be used for obtaining a reduction in congestion and gate
queues. In particular, a non-mandatory Truck
Appointment System (TAS) is considered.
Inspired by the work of Zehedner and Feillet 2013, we
propose a multi-commodity network flow model for
representing a maritime terminal. We solve a mixed
integer linear programming model based on the network
flow for determining the number of appointments to offer
for each time window in such a way to serve trucks in the
shortest time as possible, thus granting trucks a “good”
service level. Some preliminary results are presented.
Solutions show the effectiveness of the proposed model
in flattening the arrivals distribution of vehicles.
INTRODUCTION
Container maritime terminals play an important role in
the logistic networks and have to be efficient intermodal
nodes. In the last years mega vessel containerships have
been used in order to reach economies of scale by
transporting even larger numbers of containers. Thus new
problems arise in the container terminals: the need of
unloading and loading more containers in even smaller
amounts of time requires new management strategies for
avoiding congestion.
The efficient management of import and export flows is
fundamental for both the terminals and the collectivity.
Infact, congestion inside and outside the terminal may
cause serious environmental traffic problems, besides a
limitation of the efficiency of the terminals themselves.
Two strategies can be used for obtaining a reduction in
congestion and gate queues: the first strategy is the
extension of the gate capacity, generally associated to an
extension of the area of the terminal; the second strategy
concerns the Truck Arrival Management (TAM).
Strategies that are not related to TAM are, for example,
in Dekker et al. 2013, in which a chassis exchange system
is described, in Cullinane and Wilmsmeier 2011, in
which dry ports strategies are suggested as strategic
choice for maritime terminals aimed at reducing the
traffic on the roads and moving it onto the rail networks.
Dry ports strategies are particularly useful when
terminals are close to urban and suburban areas,
characterized by heavy traffic (Roso et al. 2009). In
Ambrosino and Sciomachen 2014 the problem of
locating dry ports for freight mobility in intermodal
networks is faced.
TAM strategies aim at obtaining an efficient usage of
resources inside the terminal, good service time to
clients, no congestion inside and outside the terminal.
Alessandri et al. 2008 propose a model for determining
the best allocation of the terminal resources in such a way
to optimize some key performance indexes.
TAM strategies are generally based on truck appointment
systems. In fact, usually, for what concerns the number
of trucks approaching the terminal, there are some picks
in particular hours of a day (Guan and Liu 2009), and it
is obvious that a better distribution in the arrival of trucks
at the terminal, will cause smaller queues and will
increase the efficiency of the terminal.
A Truck Appointment System (TAS) defines a maximum
number of trucks that can approach the terminal and pass
the gate during the time windows in which the working
day is split.
Truck appointment systems have been introduced by
some terminals in order to balance truck arrivals, such as
Vancouver, Los Angeles and Long Beach (Morais and
Lord 2006). The performances of these TAS are not
uniform, thus suggesting that it is necessary to implement
different TAS in accordance with specific local
conditions (Chen et al. 2013).
Huynh and Walton 2008 stress that only if there is a
correct dimension of the system, adequate to the terminal
size, such that an efficient usage of the resources of the
terminal is permitted, it is possible to obtain advantages
from TAS. The authors consider TAS an instrument for
controlling the flows and optimizing the resources usage
in the terminal; they propose a method for determining
the maximum number of vehicles that, in each time
window, can be accepted in each zone of the terminal.
Proceedings 30th European Conference on Modelling and Simulation ©ECMS Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose (Editors) ISBN: 978-0-9932440-2-5 / ISBN: 978-0-9932440-3-2 (CD)
Moreover, their study takes into account the delays and
the non-arrivals, searching for robust solutions. To the
authors’ knowledge, only another very recent work takes
into account the problem of possible truck arrival
deviation from the schedule in the appointment system:
in Li et al. 2016 a set of response strategies for
neutralizing the impact of disruptions is presented.
Among the papers investigating the problem of how to
define the appointment quota for each window, in Zhang
et al. 2013 an optimization model for determining these
quotas while minimizing the waiting time at the gate
queues and the yard waiting time, is proposed.
Chen et al. 2013 propose a time window control program
to alleviate gate congestion, that is based on three steps:
i) estimate truck arrivals based on the time window
assignment and the distribution pattern of truck arrivals
ii) estimate truck queue length using a non-stationary
queuing model iii) optimize time window in such a way
to minimize the total system cost, i.e. the truck waiting
time, the idling fuel consumption, the cargo storage time
and the storage yard fee.
In Zehedner and Feillet 2013 the authors evaluate the
impact of the TAS in the port of Marseille that uses
straddle carriers (SC) to serve trucks, trains, barges, and
vessels. They present a minimum cost multi-commodity
network flow model in which each commodity represents
a container flow from/to a transport mode. The model
simultaneously determines the number of truck
appointments to accept and the number of straddle
carriers to allocate to different transport modes with the
objective of reducing overall delays at the terminal.
In Chen et al. 2013b the problem of sizing each window
has been solved by minimizing the total number of
shifted arrivals and the total truck waiting time. The
authors show that good results in terms of truck idling
emission can be obtained by shifting also a small number
of trucks from peak to off-peak periods.
In Chen et al. 2011 another strategy used to obtain a
different distribution of truck arrivals, based on time
dependent tool pricing, is described. The authors propose
a method that firstly determines the arrival distribution
d* that minimizes the total queues time and the
disadvantages for trucks. Secondly, they try to define the
pricing tools able to modify the trucks’ behavior and to
obtain a truck arrival process equal to d*, while
minimizing the average price paid by trucks.
In Phan and Kin 2015 the focus is on the importance of
defining terminals strategies to reduce congestion by
including also decisions and requirements of trucking
companies. A mathematical model to make the
appointment system adjustments for truck arrival times
and to propose a negotiation process among trucking
companies and the terminal, has been proposed. In Phan
and Kin (2016) the authors suggest a new appointment
process by which trucking companies and terminals
collaboratively determine truck operation schedules and
truck arrival appointments.
Some papers concerning different congestion issue are,
among others, Sharif et al. 2011 which analyzes the
potential benefits of providing real-time gate congestion
information; Ambrosino and Caballini 2015 that
addresses the problem of minimizing the trucks’ service
times at container terminals while respecting certain
levels of congestion. The terminal road cycle is described
in detail and a spreadsheet is used for deciding, for each
truck having executed the check-in, if it should be
allowed to enter the terminal and, if yes, which service
level it will be given.
In this paper we investigate the management of truck
arrivals by proposing a non-mandatory TAS.
Inspired by the work of Zehedner and Feillet 2013, we
propose a multi-commodity network flow model for
representing a general terminal where the resources are
dedicated to each modal transport, and trucks
approaching the terminal can decide to book or not their
arrivals. A mixed integer linear programming model is
proposed for determining the number of appointments to
offer for each time window in such a way to serve trucks
in the shortest time as possible, thus granting trucks a
“good” service level.
The paper is organized as follows: in the next section we
present the network flow model and the mixed integer
linear programming model. Then, experimental tests on
random generated data derived by a real case study of an
Italian terminal are reported. Finally, conclusions and
further research are given.
THE NETWORK FLOW MODEL
Starting from the model in Zehedner e Feillet 2013, we
propose the following network flow for representing a
general terminal. The time horizon under investigation is
T and is split into s periods of time, i.e. T = {t1, t2,…,ts}.
Each truck approaching the terminal in the considered
time horizon is a unit of flow that enters the network and
has to exit within a given due date.
For example T can be a working day (from 6 a.m. to 10
p.m) split into 16 periods of one hour; these time periods
represent the 16 time windows in which a truck can book
the access to the terminal, of course, in accordance with
its preferred arrival time.
Let be C = {1,2,…,n} the set of n trucks that have to
approach the terminal to deliver and /or to pick up
containers during the time horizon T.
Let us introduce the following notation used to
characterize each truck k ϵ C:
pk ∀kϵC represents the number of operations that
truck k has to execute inside the terminal (i.e. pk=2 if
truck k has to deliver an export container and to pick
up one import container). The maximum value of pk
is 4 (i.e. 2 export 20’ containers to deliver and 2
import 20’ containers to pick up).
rk such that t1 ≤ rk ≤ ts, ∀kϵC, represents the slot of
time in whick truck k approaches the terminal;
dk such that rk ≤ dk ≤ ts, ∀kϵC, is the due time for
vehicle k; this means that truck k has to leave the
terminal, having executed all pk operations, within
slot dk .
Let us define the graph G = (V, A) used for representing
the terminal road cycle as described in Ambrosino and
Caballini 2015 i.e. truck arrivals, the gate queue, the
truck service inside the terminal and, finally, the truck
exits.
V is the set of vertices given by the union of the following
subsets V = O ∪ G ∪ У ∪ S where:
O = {Ok | k ϵ C }, where Ok represents the origin node for
truck k;
G = {Gt | t ϵ T }, where Gt represents the time period t in
which the trucks are at the gate queue;
У = {Уt | t ϵ T } where Уt represents the time period t in
which the trucks are inside the terminal for executing the
unloading/loading operations;
S = {Sk | k ϵ C } where Sk represents the sink node for
truck k.
A is the set of arcs given by the union of the following
subsets A = A1∪A2∪A3∪A4∪A5 where:
A1 = {(Ok, Gt) | k ϵ C, t = rk}: for each truck k there is a
link between its origin node (Ok) and the gate queue node,
related to the period of time t equal to the truck arrival
time (rk).
A2 = {(Gt, Gt+1) | 1 ≤ t ≤ ts-1} is the set of arcs connecting
each gate queue node Gt with node Gt+1; these arcs are
used for representing the trucks remaining in the gate
queue from time period t to t+1;
A3 = {(Gt, Уt) | t ϵ T} for each time period t there is an
arc connecting each node Gt with the corresponding
node Уt ; these arcs are used for representing trucks that
in time period t enter into the terminal through the gate;
A4 = {(Уt, Уt+1) | 1 ≤ t ≤ ts-1} is the set of arcs connecting
each node Уt with node Уt+1; these arcs are used for
representing the trucks remaining inside the terminal for
completing the unloading/loading operations from time
period t to t+1;
A5 = {(Уt, Sk) | k ϵ C, rk ≤ t ≤ dk} each truck k can be
inside the terminal in time period t such that rk ≤ t ≤ dk,
thus there are some links connecting nodes Уt, of these
time periods to the sink node Sk; these arcs are used for
representing the truck exit.
Each truck k is here considered as a unit of flow, that has
to go from the origin node Ok to the node Gt with t = rk .
After that there are two possibilities: 1) the truck k is
served by the gate and enters the terminal, that is the flow
enters into the corresponding node Уt; 2) the truck k
remains in the gate queue, that is the flow enters into node
Gt+1. When the truck is inside the terminal, it has to pass
from a node Уt to the next Уt+1 until it has finished all
terminal operations (pk); after that, it will leave the
terminal reaching node Sk.
In Figure 1 is depicted a network flow for representing
three trucks arriving at the terminal respectively in r1=1,
r2=2, and r3=2, having as due time d1=3, d2=4 and d3=3.
Figure 1: the network flow for 3 trucks
The Mixed Integer Linear Programming Model
The main aim of this work is to use the network flow in
order to determine the best way for serving trucks that
enter the terminal, i.e. to minimize the truck service time
given by the total time spent by each truck inside the
terminal and the total time spent in the gate queue.
Let us introduce the notation useful for presenting the
mixed integer linear programming (MILP) model here
proposed.
Let be:
akijϵ{0,1}, k ϵ C, (i,j) ϵ A1 such that {i= Ok, j=Gt| t
=rk}: akij = 1 if truck k reaches the terminal and goes
to the queue gate.
qkijϵ{0,1}, k ϵ C, (i, j) ϵ A2 such that{i = Gt | rk≤ t
≤dk-1, j=Gt+1 | rk≤ t ≤dk-1}: qkij =1 if the unit of flow
(the truck k) passes through the arc (i, j) ϵ A2, that is
the truck k remains in the queue from time period t
until time period (t+1).
ekijϵ{0,1}, k ϵ C, (i, j)ϵA3 such that {i=Gt | rk≤ t ≤
dk, j=Уt | rk ≤ t ≤ dk}: ekij =1 if the unit of flow (the
truck k) passes through the arc (i, j) ϵ A3 that is the
truck k at time period t enters the terminal.
ykijϵ{0,1}, k ϵ C, (i, j) ϵA4 such that{i = Уt |≤ t ≤dk-
1, j=Уt+1 | rk≤ t ≤dk-1}: ykij =1 if the unit of flow (the
truck k) passes through the arc (i, j) ϵ A4, that is the
truck k remains inside the terminal from time period
t until time period (t+1) for concluding
unloading/loading operations.
xkijϵ{0,1}, k ϵ C, (i, j) ϵA5 such that {i = Уt | rk≤ t
≤dk, j=Sk }: xkij =1 if the unit of flow (the truck k)
passes through the arc (i, j) ϵ A5, that is the truck k in
time period t has completed its pk operations and
leaves the terminal. The unit of flow k reaches its
sink node.
bkϵ{0,1}, k ϵ C, is equal to 1 if vehicle k has a
booking.
gt ≥ 0, gt ϵN, t ϵ T, is the set of integer variables
representing the number of gate lanes that are
devoted to trucks having a booked appointment for
time period t. Note that this set of variables is useful
for defining the size of the booking system.
zkϵ{0,1}, k ϵ C is the set of auxiliary variables used
for linearizing a set of constraints in the MILP
model: zk= akij*bk.
Let us now introduce the parameter used in the model:
c1kij , k ϵ C, (i, j) ϵ A2 such that {i = Gt |rk≤ t ≤dk-1,
j=Gt+1 | rk≤ t ≤ dk-1}: is the cost for having truck k in
the gate queue from time period t to t+1;
c2kij, k ϵ C, (i, j) ϵ A5 such that {i =Уt |rk≤ t ≤dk, j=Sk
}: is the cost associated to truck k that leaves the
terminal. The main aim is to serve each vehicle in
the lower time as possible. The lower is the
difference between the time period t in which the
truck leaves the terminal and its due time dk, the
higher is this cost;
k represents the benefit for having truck k booked;
lbU is the maximum number of gate lanes that can
be reserved to booked vehicles;
is the maximum number of vehicles that can be
inside the terminal;
pt is the maximum number of unloading and loading
operations that can be executed during time period t;
b is the target service time for booked trucks fixed
by the terminal management, i.e. average time that
booked trucks may spend in the terminal. This
average time is computed as time in the gate queue
and service time for entering the terminal.
represents the number of vehicles that can be
processed by each gate lane in each time period.
The resulting model is the following:
M1)
𝑀𝐼𝑁 ∑ ∑ 𝑐1𝐺𝑡,𝐺𝑡+1𝑘 ∗ 𝑞𝐺𝑡,𝐺𝑡+1
𝑘(𝐺𝑡,𝐺𝑡+1)∈𝐴2𝑘∈𝐶 +
+∑ ∑ 𝑐2𝑌𝑡,𝑆𝑘
𝑘 ∗ 𝑥𝑌𝑡,𝑆𝑘
𝑘 (𝑌𝑡,𝑆𝑘)∈𝐴5−𝑘∈𝐶 ∑ 𝛼𝑘 ∗ 𝑏𝑘𝑘∈𝐶 (1)
s.t. 𝑎𝑂𝑘,𝐺𝑡𝑘 = 1 ∀ 𝑘 𝜖 𝐶, 𝑡 = 𝑟𝑘 (2)
∑ 𝑥𝑌𝑡,𝑆𝑘
𝑘(𝑌𝑡,𝑆𝑘)𝜖𝐴5
= 1 ∀ 𝑘 𝜖 𝐶 (3)
(𝑎𝑂𝑘,𝐺𝑡𝑘 + 𝑞𝐺𝑡−1,𝐺𝑡
𝑘 ) = (𝑞𝐺𝑡,𝐺𝑡+1𝑘 + 𝑒𝐺𝑡,𝑌𝑡
𝑘 ) ∀ 𝑘𝜖𝐶,
𝑡|𝑟k ≤ 𝑡 ≤ 𝑑k (4)
(𝑒𝐺𝑡,𝑌𝑡𝑘 + 𝑦𝑌𝑡−1,𝑌𝑡
𝑘 ) = (𝑦𝑌𝑡,𝑌𝑡+1𝑘 + 𝑥𝑌𝑡,𝑆𝑘
𝑘 ) ∀𝑘𝜖𝐶,
𝑡|𝑟k ≤ 𝑡 ≤ 𝑑k (5) 𝑧𝑘 ≤ 𝑎𝑂𝑘,𝐺𝑡
𝑘 ∀ 𝑘 𝜖 𝐶, 𝑡 = 𝑟k (6) 𝑧𝑘 ≤ 𝑏𝑘 ∀ 𝑘 𝜖 𝐶 (7)
𝑧𝑘 ≥ 𝑎𝑂𝑘,𝐺𝑡𝑘 + 𝑏𝑘 − 1 ∀ 𝑘 𝜖 𝐶, 𝑡 = 𝑟k (8)
𝑧𝑘 ≤ 𝑒𝐺𝑡,𝑌𝑡𝑘 ∀ 𝑘 𝜖 𝐶, 𝑡 = 𝑟k (9)
𝜇𝑏 ≥ 1
𝑔𝑡∗− ∑ 𝑧𝑘kϵC
∀ 𝑡 (10)
𝑔t ≤ 𝑙𝑏𝑈 ∀ 𝑡 (11)
∑ 𝑦𝑌𝑡,𝑌𝑡+1𝑘 ≤ 𝜋 𝑘𝜖𝐶 ∀ 𝑡 | t ≤ |T|-1 (12)
∑ 𝑝k ∗ 𝑥𝑌𝑡,𝑆𝑘
𝑘 ≤ 𝜋𝑡𝑝
𝑘𝜖𝐶 ∀ 𝑡 (13)
Objective function (1) minimizes the costs associated to
the trucks in the queue at the gate and the costs for
serving the truck near their due time, while trying to
maximize the total number of booked vehicles.
Constraints (2) force each vehicle k to arrive at its
preferred time rk, i.e. each truck k leaves its source node
in rk, while constraints (3) ensure to each vehicle k to
reach its sink node.
(4) and (5) are the flow conservation constraints for nodes
of set G and Y, respectively.
Constraints (6), (7), (8) define variable zk as the product
of variables akij and bk in order to preserve linearity in the
model. These constraints, together with constraints (9),
replace the following ones that are necessary to guarantee
that a booked truck k enters the terminal as soon as it
arrives at the gate:
𝑎𝑂𝑘 ,𝐺𝑡𝑘 ∗ 𝑏𝑘 ≤ 𝑒𝐺𝑡,𝑌𝑡
𝑘 ∀ 𝑘 𝜖 𝐶, 𝑡 = 𝑟𝑘
Constraints (10) limit the time spent in the queue outside
the terminal by booked vehicles, this maximum queue
time is decided by the terminal operator and it is set by
parameter µb .
Set of constraints (11) bounds the number of gate lanes
reserved to booked vehicles, while constraints (12) limit
the number of vehicles inside the terminal from time
period t to the following t+1.
Lastly, constraints (13) represent the terminal capacity
for handling operations: the total number of operations
executed in each time period t must be no greater than the
terminal handling capacity.
An Extension of the Previous Network Flow Model
A drawback of model M1 is the following: a truck can
not book the access to the terminal in a time period
different from its preferred arrival time rk. Anyway, for
increasing the capability of the booking system of
modifying the arrival process to the terminal it is
necessary to give the possibility to the appointment
system to book for period of times different from
preferred truck arrivals.
The disadvantage for the truck operator that is obliged to
modify his behavior, will be compensated by the
advantages derived by having fixed and known the
service time at the terminal. Moreover, the allowable
deviation between preferred and booked time period is
limited.
Thus, we have modified both the network flow and the
model in such a way to permit to a truck k to book an
appointment for a time period different from rk.
In Figure 2 the new network flow is depicted.
Figure 2: example of network flow for one truck with a
maximum absolute deviation of 2 periods
Let be the maximum deviation from the preferred
arrival time (rk) of vehicle k, thus follows:
A1 = {(Ok, Gt) | k ϵ C, rk - t rk+};
A5 = {(Уt, Sk) | k ϵ C, rk - ≤ t ≤ dk};
akijϵ{0,1}, k ϵ C, (i,j) ϵ A1 such that {i= Ok, j=Gt|
rk - t rk+};
xkijϵ{0,1}, k ϵ C, (i, j) ϵA5 such that {i = Уt | rk -
≤ t ≤dk, j=Sk };
qkijϵ{0,1}, k ϵ C, (i, j) ϵ A2 such that{i = Gt | rk -
≤ t ≤dk-1, j=Gt+1 | rk - ≤ t ≤dk-1};
ekijϵ{0,1}, k ϵ C, (i, j)ϵA3 such that {i=Gt | rk - ≤ t
≤ dk, j=Уt | rk - ≤ t ≤ dk};
ykijϵ{0,1}, k ϵ C, (i, j) ϵA4 such that{i = Уt | rk - ≤
t ≤dk-1, j=Уt+1 | rk - ≤ t ≤dk-1};
zk is changed as zki such that k ϵ C and i = Gt| rk-Δ ≤ t
≤ dk, to better explain the product akij * bk including
the time of arrival at the gate.
Constraints of model M1) defined for t such that 𝑟k ≤𝑡 ≤ 𝑑k , must now be defined for 𝑟k − Δ ≤ 𝑡 ≤ 𝑑k ,
and those defined for 𝑡 = 𝑟𝑘 must now be defined for
𝑟k − Δ ≤ 𝑡 ≤ 𝑟k + Δ. Moreover, constraints 2) must be
modified as follows:
∑ 𝑎𝑂𝑘,𝐺𝑡𝑘
(𝑂𝑘 ,𝐺𝑡)∈𝐴1
= 1 ∀ 𝑘 𝜖 𝐶
Finally, in the new model (from now we will refer to it as
M2) we try to minimize also the deviation between the
trucks appointments and their preferred arrival time (rk).
For this reason we define:
β the cost paid for having modified the arrival time
at the terminal.
The new component of the objective function is:
𝛽 ∗ ∑ ∑( |𝑡 ∗ 𝑧𝑖𝑘 − 𝑟𝑘 |)
𝑖=𝐺t𝑘∈𝐶
COMPUTATIONAL RESULTS
In this section we report the results obtained by solving
model M2 for some random generated data derived by a
real case study of an Italian terminal.
Figure 3 shows the arrival distribution in a working day
of the terminal used for generating data. As usual this
distribution presents a peak of the truck arrivals.
Figure 3: arrival distribution
In this experimental campaign, we have considered a
wide range of different scenarios.
First of all, we have analyzed the differences between
implement a 1-hour time window and a 2-hours time
window, where the latter one offers an easier
organization for haulers, at the cost of less efficiency for
the terminal.
Secondly, we have simulated three different possibilities
for the daily total arrival of trucks: in the first case the
total number of vehicles results less than the average of
the work situation (1.800 trucks per day), in the second
one the total number of vehicles results in average with
the work situation (2.000 trucks per day) and in the last
scenarios the total number of vehicles results higher than
the average work situation (2.200 trucks per day).
To deeply analyze the behavior of the model, and mostly
to validate it, we have also generated scenarios by
changing the number of operations to be executed at the
terminal by trucks.
Moreover, to study how the policy of assured maximum
time elapsed in the queue impacts on the model solutions,
various values of b have been applied.
Lastly, we have used three different average times for
gates operations (λ) to identify the operational target
terminal handlers should aim for.
Each scenario has been named following the
nomenclature shown in the Table below.
Table 1: Scenarios nomenclature
1 2 3 4
A Time windows width 1 hour 2 hours
B Total daily arrivals 1800 2000 2200
C Number of operations (partition) 50/50/0/0 40/40/20/0 40/40/15/5
D Maximum time in queue 10 minutes 20 minutes 30 minutes 40 minutes
E Handling capacity (number of vehicles served) 60 90 120
Value
All generated scenarios have been solved up to optimality
by model M2.
By varying b, we can observe in Figure 4 little changes
in the optimal arrival distributions.
Solutions obtained by imposing a maximum time to
spend in the gate queue for booked trucks of 40 minutes
do not differ much from those obtained by having this
limit equal to 10 minutes. Thus terminal operator can
persuade hauler to book their entry by promising a
smaller amount of time spent in the queue while limiting
the risks of operational problems.
Figure 4: arrival distribution varying b
More interesting is the study of the solutions obtained by
varying parameters . As shown in Figure 5 when the
time required for serving one truck at the gate passes
from 60 to 45 seconds, a significant redistribution of
trucks arrivals can be observed, while passing from 45 to
30 seconds significant changes are no more evident.
This is due to the fact that in these scenarios, the number
of entrances is limited by terminal handling capacity,
where in the case with 45 seconds both constraints, time
spent in queue and handling capacity, affect the solution.
Figure 5: arrival distribution varying
Increasing the number of operations to be executed at the
terminal by trucks, pushes the model to increasingly
modify arrivals distribution.
A lower number of operations associated to each truck
allows the terminal to easily handle the whole traffic,
especially with a low number of daily arrivals, while the
terminal reaches its full handling capacity when an higher
number of operations is considered. The graph of Figure
6 shows how the model modifies the arrival distributions.
Figure 6: arrival distribution varying the number of
operation to execute
Similarly, the model increases its action in redistributing
trucks arrivals at terminal when the daily total number of
trucks (|C|) increases, as shown in Figure 7.
Figure 7: arrival distributions for different and
increasing |C|
CONCLUSIONS AND FUTURE WORKS
In order to tackle the problem of increasing queues
outside container terminals, the implementation of a non-
mandatory truck appointment system is studied.
Optimal size of the system, capable of decreasing
congestion while trying to impact as little as possible
hauler operational plans, is obtained by a mixed integer
linear optimization model, used for defining optimal
flows in the network flow model which simulates the
operability of a container terminal during a workday.
Solutions found demonstrate the effectiveness of the
model to re-shape arrivals distribution and to adapt to
shifting conditions, both external (number of arrivals,
number of operations to be executed inside the terminal)
and internal (mostly operational target, such as maximum
time spent in the queue by booked vehicles and average
service time at gates).
Future developments focus on the modification of the
network flow, in such a way to better simulate the
behavior of trucks once inside the perimeter of a
container terminal. For this reason the width of the time
windows will be decreased. Moreover, a limitation on
the time spent in queue for not booked vehicles will be
included in the model.
The optimization model will be developed using C#
programming language, this addition allows the
simulation of a wider number of scenarios for both a
better understanding of the problem and validating the
model.
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AUTHOR BIOGRAPHIES
DANIELA AMBROSINO is assistant
professor of Operation Research at the
University of Genoa, Italy. She is
teaching Operation Research for
management and Optimization and
Simulation for maritime transport.
Her main research activities are in the field of distribution
network design and maritime logistic. Her e-mail address
LORENZO PEIRANO is postgraduate in Maritime
Economics and Ports Management at the
University of Genoa, Italy. He
occasionally collaborates with the
University of Genoa for research
activities in maritime logistics. He is
working at Aldieri Autotrasporti S.p.A.
(Italy) as airfreight forwarder.
This paper is mainly inspired by his postgraduate degree
dissertation awarded by the Italian society of Operational
Research in September 2015.
His email address is [email protected]